Inverses of equations and domain/range help?!?

Find the equation for the inverse of-

1. g(x)=x^2+8 , x>=0

2. h(x)=(x+3) / (4x-2)

Find the domain and range of f in interval notation

f(x)=-2x^2+12x-10

Top 1 Answers

A few days ago

gang$tahtooth

Favorite Answer

To find the inverse you need to switch x and y. I’d just replace g(x) and h(x) with y to make it easier.

1. y=x^2+8

x=y^2+8

x-8=y^2

+/- sqrt (x-8)=y=g^(-1)(x)

2. y=(x+3)/(4x-2)

x=(y+3)/(4y-2)

4xy-2x=y+3

4xy-y=2x+3

y(4x-1)=2x+3

y=(2x+3)/(4x-1)=h^(-1)(x)

For the domain and range you need to find what x and y can and cant be for the function to be a function.

in this one x can be anything right? so

D: (-infinity, infinity)

this is an upside down parabola so the vertex (3,8) will be the maximun

R: [8, -infinity)

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